e ¼ 2:67p—0:46 ð20Þ

where p is the pressure in kPa。 The critical pressure for compression is around 17 kPa, under which the porosity of the algal cake-layer is a constant。 With the estimated mean porosity of the algal cake- layer, the volumetric flow-rate of filtrate water and processing capacity of the filter under various operating conditions can be eval- uated using Eqs。 (17) and (18)。

Another important parameter of algal cake-layer is cake-layer pore size。 As shown in Fig。 2, the filtrate channel in the  cake-layer is actually a network structure。 This situation may also be compli- cated with the network clogging。 Network clogging may be caused by small-sized algae in the algal feed, and/or by the extracellular organic matter (EOM) [32] released by algae particularly in the case of high pressure filtration。 Obviously, clogging of the network would result in a reduced cake-layer porosity and pore size。 Note the probability of clogging in the cake-layer is impossibly difficult to model。 An alternative approach is taken in this modeling。 By linking the  clogging to the alternation in  the cake-layer     porosity

In Fig。 1, supposing the filtration is performed at the vacuum

pressure of pfiltration, the total energy consumed by the water pump is thus

1

Wwater  pump  ¼ Ffeedð1 — /Þðpambient  — pvacuum  receiverÞ g ð25Þ

pvacuum    receiver  ¼ pfiltration  — qwater gR — Dpresistance ð26Þ

Dpresistance   ¼ 0:5qwater gR ð27Þ

where R is the radius of the filter drum, and g is the energy effi- ciency of the water pump。 As depicted in Fig。 1, the pressure head loss due to the piping resistance is not a constant since the flow-rate of the filtrate water passing through the drum piping varies throughout the filtration process。 The piping in the filtration system is relatively short and large piping diameter can be chosen to avoid any significant head loss。 For simplicity, according to the above rational, this resistance is assumed to be a constant equivalent to 50% of the static pressure difference in the system。 Strictly speaking, the static pressure difference created by the water present in the connecting piping in the drum is also not a constant, dependent upon the location of the connecting piping within the filtration zone。 As shown in Eq。 (26), the maximal value (R) was used to esti- mate this static pressure。 A simple geometric calculation based on the drum in Fig。 1 shows that no significant error was introduced with this treatment。

The vacuum pump in the system is intended to maintain a steady vacuum pressure in the vacuum receiver to ensure a contin- uous water flow in filtration。 In the algae dewatering zone, the   air

P。 Shao et al。 / Chemical Engineering Journal 268 (2015) 67–75 71

flow passing through the cake-layer will also be excavated with the vacuum pump。 Evaluation of energy consumption of the vacuum pump needs to estimate this  air  flow-rate,  which  is determined by the Hagen–Poiseuille equation [12,29,34] as shown in Eq。   (28),

industrial project。 Supposing the  labor  requirement  of  a process is proportional to its scale,  and  the  salary  of  the  worker  is 50 kUS$/yr, the labor cost allocated to this project can be deter- mined by

The overall algae-dewatering cost should include all the cost

where l is the viscosity of air, p0 is the atmospheric pressure, and a is the tortuosity of pores in the cake-layer。 Therefore, the energy consumption of the vacuum pump for the isentropic compression of the air flow is evaluated by Eq。 (29)  [35],